Скачать или смотреть Solve Linear Programming in 2 Ways | Graphical & GAMS | Feasible Line Example

Welcome to this step‑by‑step Linear Programming (LP) tutorial, where we solve a unique optimization problem using two powerful methods: the Graphical Method and GAMS (General Algebraic Modeling System).

📌 The Problem
We aim to minimize the following objective function:

Max Z=4x1+2x2
s.t.
5x1+2x2=l=20
2x1+3x2=g=12
4x1-x2=0
x1,x2=g=0

Special Note: In this example, the feasible region is not a polygonal area — it lies entirely along a single line. This makes it an interesting case to analyze, both visually and computationally.

💡 What You Will Learn
In this video, you’ll learn:
Graphical Solution for LP Problems
How to plot constraints and the feasible line in a 2D space
Finding the optimal point visually
Understanding the impact of a “feasible line” case on graphical interpretation
Solving the Same Problem Using GAMS
Writing the LP model in GAMS syntax
Running the model and interpreting the solver output
Comparing results with the graphical method

🎯 Why This Video Is Worth Your Time
Covers two complementary approaches in one tutorial
Perfect for beginners and intermediate learners in Operations Research
Explains a special case where the feasible region is a line — a scenario often overlooked in standard LP examples
Shows both manual visualization and professional solver usage
Great for coursework, self‑study, and research

🧠 Who Should Watch
University students in engineering, economics, mathematics, or management
Professionals working in optimization, logistics, planning, or resource allocation
Anyone interested in learning practical problem‑solving techniques in LP


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